TOPOLOGICAL EVALUATION OF FEEDBACK MATRICES IN MULTIPLE-LOOP FEEDBACK-AMPLIFIERS

Topological formulas for the evaluation of the elements of the return difference and the null return difference matrices of a multiple-loop feedback amplifier are presented. They are expressed in terms of the directed-tree and directed-two-tree admittance products in the associated digraph. In the situation where the controlling parameters of all the controlled sources are chosen as the elements of interest, the associated digraph is simply the graph representing the feedback amplifier after the independent source and controlled sources have been removed. The significance of the present approach is that it not only provides a short-cut for the evaluation of the feedback matrices, but also gives an insight into the behavior of the feedback amplifier under consideration. © 1979.